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A Major Qualifying Project completed in partial fulfillment

of the Bachelor of Science degree at

Worcester Polytechnic Institute, Worcester, MA

By

Patricia MacKoul (Reed)

Date:

29th of April, 2014

Richard S. Quimby, Ph.D.

Worcester Polytechnic Institute

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The purpose of this project was to obtain the absorption cross-section, emission cross-

section, and fluorescence lifetime of various thulium (Tm+) doped host crystals at the 800nm

transition. Four crystals were tested: YVO4, YLiF, YAlO, and YAG. Two different

spectrometers were used to obtain the absorption measurements, and the emission spectra was

both measured and calculated using the reciprocity method. Utilizing the rate equations and

analyzing the gain coefficient, each crystal was analyzed to determine the pump power at which

gain saturation would occur – where the crystal becomes less effective at absorbing pump power

and the gain coefficient starts to approach a maximum. In the case of the Tm:YLiF and

Tm:YAG, gain saturation occurs at approximately 40kW (for a rod of diameter 0.4 cm). For the

Tm:YVO4 gain saturation occurs at approximately 100kW and for Tm:YAlO, 90kW. Using the

measured lifetime data, the overall quantum efficiency of each crystal was determined. Other

figures of merit that were determined for each crystal are the maximum gain coefficient per total

dopant concentration, the gain coefficient per unit of absorbed pump power, and the gain

coefficient per unit of incident pump power. After analyzing the crystals using these methods,

the determination was made that for this transition, the Tm:YLiF would be the best candidate

crystal to use for further prototyping. The Tm:YLiF has a quantum efficiency of 91%, which

means that most of the thulium ions in the upper laser level decay radiatively, resulting in less

heat generated in the crystal. The Tm:YLiF also experiences net gain at a lower threshold pump

power than the other crystals analyzed, and reaches gain saturation before both the Tm:YVO4

and Tm:YAlO.

5

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I would like to thank the following individuals and organizations for their contributions to this

Major Qualifying Project:

�� Professor Richard S. Quimby, for his guidance, his continuous feedback on my project,

and the opportunity to work in WPI’s IPG Photonics® laboratory.

�� Dr. T.Y. Fan for providing me the idea for this project, his encouragement and guidance,

and allowing me the opportunity to use the facilities at MIT Lincoln Laboratory.

�� The Physics Department at WPI, friends and faculty, thank you all for your friendship

and assistance throughout my time here at WPI.

�� Everyone at MIT Lincoln Laboratory – especially the Laser Technology and Applications

group – for their support, encouragement, and the opportunity to achieve a life goal.

�� My family and friends, especially my parents, for their love, wisdom, and

encouragement.

6

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8

1��

Thulium doped lasers have been demonstrated in crystalline host materials at various

wavelengths. The need exists for higher efficiency lasers that produce average and peak power

than previously demonstrated. The 3H4 –

3H6 transition with a nominal lasing wavelength of

820nm is a possibility for this increase in power due to its ability to be pumped with an efficient

diode laser in the 780nm-800nm range. The upper state has a lifetime with a magnitude on the

order of a millisecond which allows the population to increase and energy to be stored in this

level (see Figure 1).

Figure 1. Thulium’s emission wavelengths of the metastable levels

Lasing at this nominal wavelength has been effectively demonstrated using thulium-

doped fluorozirconate (Tm:ZBLAN) fibers. Experiments showed successful lasing at the 820nm

transition. Initially, the limitations of that material only allowed for low average power

demonstrations only (Carter, 1991). Since that time, further advancements have been made and

higher power has been achieved. For the applications discussed below, much higher average

power and peak power will be needed.

An efficient laser at this particular wavelength could be utilized in many applications. At

820nm, the transmission through water is relatively high comparatively (see Figure 2) but the

second harmonic of this wavelength range occurs near the minimum absorption line for clear

ocean water.

9

Figure 2. Absorption vs. wavelength for water

Another example, power-beaming, would allow for transference of power from the laser

to another system. Power-beaming would require the use of photovoltaic cells, and the peak

conversion efficiency of single-junction GaAs cells is near the 820nm range of interest (see

Figure 3).

Figure 3. Photovoltaic efficiency vs. wavelength (Materion,2014)

Although the metastable 3H4 level has a lifetime on the order of a millisecond magnitude,

which allows for excellent energy storage, a problem arises in this transition because of an

intermediate level which has a lifetime of approximately 10 milliseconds. This long lifetime

causes population trapping in the intermediate level and decreases the efficiency of lasing at the

10

desired 3H4 –

3H6 transition. In order to efficiently lase on this transition, this population trapping

must be decreased.

Due to the range of lifetimes for different host materials, an examination into various

properties such as the absorption and emission cross-sections and lifetimes for each applicable

host material must be performed. Host materials chosen for analysis are: YLiF (Yttrium Lithium

Fluoride), YVO4 (Yttrium Vanadate), YAlO (Yttrium Aluminum Oxide), and YAG (Yttrium

Aluminum Garnet). Due to the high costs of building a high power laser system, it is necessary

for spectroscopic analysis to help determine the most suitable host material for a prototype

system. Using the data acquired and inserting into the rate equations allows for the level

concentrations to be determined at various powers. With these level concentrations determined,

the gain coefficient at the desired emission wavelength (820nm) can be calculated as a function

of power (both pump and absorbed) and provide us with a means to comparatively analyze the

transition. Based on this analysis, a recommendation can be made on which crystal or crystals

should be used for further testing.

11

3��)+��

The following sections examine how lasers work in general, and with special attention to

the thulium transition this project is based upon. Included are explanation of the Judd-Ofelt

theory and branching ratios, and the part cross-relaxation plays in this laser transition. With this

information, a further understanding of the rate equations used to analyze the transition can be

achieved. The various host materials are also briefly explained.

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Due to the laws of energy conservation, atoms require energy to move to a higher energy

level and also need to release energy to fall to a lower energy level. Stimulated emission is one

of the two processes by which an atom, that is located in a higher energy level than the ground

state, emits energy due to an incident photon. The emitted energy is emitted in the form of

another photon and that photon’s energy will equal the energy of the incident photon.

Spontaneous emission is a similar process, but does not require an incident photon (Hecht,

2008). In order for the stimulated emission rate to be greater than the rate of absorption, there

must be a population inversion in the upper energy level. A population inversion occurs when the

population of the higher energy level is greater than the lower energy level. If the population

inversion ceases, then the lower state is more likely to absorb any photons and the net gain will

become negative which implies more absorption is occurring instead of emission (Hecht, 2008).

The gain coefficient is given by the equation below:

�� = �� − �� Where �� is the number of ions per unit volume in the upper level, �� is the emission

cross section at the desired emission wavelength, �� is the population (number of ions per unit volume) in the ground state, and ��is the absorption cross section at the desired emission wavelength. If the gain coefficient is negative, net absorption is occurring. If it is positive, net

emission is occurring (Quimby, 2006).

12

The amount of time it takes a certain fraction of the atoms to fall from one excited state to

a lower one, without stimulation, is known as the lifetime. The lifetime is determined by both the

non-radiative and radiative decay of the atoms to the lower state. Non-radiative decay is a

vibrational emission which causes the host material to heat up by releasing phonons. Radiative

emission results in a photon (Hecht, 2008).

In the case of the transition of thulium ions, when they decay from the excited 3H4 level,

they quickly decay (spontaneously and non-radiatively) from the 3H5 to the

3F4 level; at the

3F4

level there is a long fluorescence lifetime of approximately 10ms (see Figure 4). The long

lifetime causes the population at this level to increase faster than it depletes. Continuous lasing is

still possible, even if the populations N4 and N1 are equal as long as the emission cross section is

greater than the absorption cross section at the signal wavelength.

Figure 4. Thulium’s lifetimes of the metastable levels

Another problem that occurs with thulium ions lasing at this transition is cross-relaxation,

the process where an ion in the upper state transfers some of its energy to another ion in the

ground state, causing both to end up in the metastable 3F4 level. This process of cross-relaxation

would be beneficial to lasing if we were looking to lase at 2 microns. However, it is detrimental

to the 800nm transition, because it adds more ions to the energy level with the longest lifetime

that we are attempting to mitigate. The effects of cross-relaxation are increased with higher

doping concentrations because an increase in ion density means an increase in the probability of

13

an ion in the upper state transferring some of its energy to an ion in the lower state. For the

purpose of this project, we will ignore the effects of cross-relaxation because at the concentration

we are working with, the effects are minimal.

The purpose of the absorption and emission measurements is to find the gain coefficient,

which as explained earlier, is found by analyzing both the absorption and emission cross-sections

and the ion populations per level of each host material. By solving the rate equations explained

below in the steady state (level concentration does not change with respect to time) the gain

coefficient can be determined.

The easiest way to analyze the transition is by use of rate equations. Rate equations state

the rate at which the population of each level changes with respect to time. By analyzing each

level individually, every factor – such as pumping power, pump wavelengths, emission

wavelengths, and lifetimes – that cause a change in the population of a particular energy level

can be thoroughly examined (Quimby, 2006). In order to successfully predict a laser system’s

behavior with rate equations, the following variables must be known: absorption and emission

cross-sections, energy transfer rates, radiative and non-radiative relaxation rates, and branching

ratios (Walsh, 1998).

4��5��7�3��+�!��

Transitions of rare-earth ions (such as thulium) in a solid-state medium are generally

electric dipole and magnetic dipole in nature. The Judd-Ofelt theory is used to describe the

intensities of these transitions in rare earth ions such as thulium. The theory is used to determine

transitional probabilities for each manifold to manifold transition. For the purpose of this project,

we referenced literature that utilized the Judd-Ofelt theory to determine the transitional

probabilities (Walsh, 1998).

The branching ratio is defined as the fraction of photon flux which goes from the upper

energy manifold to a lower energy manifold. It is the probability of an atom decaying

(radiatively) from the upper manifold to a particular lower manifold divided by the sum of all the

14

probabilities of emission to all the lower manifolds (which equal unity or 1). It can be calculated

by the following equation:

�� = ��∑ �� Where��, represents the radiant intensity as a function of wavelength��,�� represents

the upper manifold and�� represents the lower manifold (Walsh, 1998). In the case of the Thulium

transition studied in this project, there are three possible lower manifolds the atom can decay to –

the 3H5,

3F4, and

3H6 manifolds. The

3H5 immediately decays non-radiatively because it has a

very high radiative lifetime and very low non-radiative lifetime; therefore, the branching ratio for

this level can be combined into the ratio for the 3F4 level. For the purpose of this project, the

branching ratios were obtained from previous research (see Table I – Host Materials).

��!��8��7%��

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Rate equation analysis is necessary for modeling every laser system. By calculating the

rates at which the individual energy levels are populated and unpopulated, the change in the net

gain can be evaluated for various pumping powers. These rate equations can serve as a blueprint

for plugging in the measured or obtained data and solving for the gain coefficient as a function of

pump power (Quimby, 2006). With that information, the different host materials can be

compared to determine the best host for the desired application.

The rate equations for the 3H4 – 3H6 transition that will be used for analysis have been

determined to be as follows:

�� = ��ℎ�� − �� − ��ℎ�� − �� − �� !� − �� "!� ��#�� = �#�� !� + �� "!� − �# !# − �# "!# ��%�� = �%�� !� + �# "!# − �% !% − �% "!%

15

�� = ��ℎ�� − �� − ��ℎ�� − �� + �� !� + �% % Where ��, �#, �%, �� are the populations of each level with ��representing the population of the 3H4 level, �# is 3H5, �% is 3F4, and �� is 3H6 and the sum of these populations is the concentration of dopant (�� + �# + �% + �� = �); N is a known value provided in Table I.

Often the rate equations can be further understood by using notation designating the

pump rates and emission rates. The pump rate is defined as the probability per unit time that an

ion will be pumped from its current level, it is denoted by:

'� = ��ℎ�� Where �� in the intensity of the pump light, �� is the cross section at the pump

wavelength, and ℎ�� is the energy of a pump photon. The pump absorption rate is designated as: '�� = ��ℎ��

This is the probability per unit time that an ion will be absorbed into an upper state due to

an incident pump photon. The pump emission rate is designated as:

'� = ��ℎ�� This is the probability per unit time that an ion will be emitted into a lower state due to an

incident pump photon. Similarly, the signal transition rate is defined as the probability per unit

time that an ion will make an upward or downward transition due to signal light, and it is

denoted by:

'� = ��ℎ�� Where �� in the intensity of the signal light, �� is the cross section at the signal

wavelength, and ℎ�� is the energy of a signal photon. The signal absorption rate is designated as:

16

'�� = ��ℎ�� This is the probability per unit time that an ion will make a transition to an upper state

due to a signal photon. The signal emission rate is designated as:

'� = ��ℎ�� This is the probability per unit time that an ion make a transition to a lower state due to a

signal photon (Quimby, 2006).

The rest of the variables in the rate equations are defined as follows: τ is the lifetime

(designated as either radiative or non-radiative – if not designated assume total fluorescence),

and β is the branching ratio explained in the previous section.

The relationship between the total fluorescence lifetime and the non-radiative and

radiative lifetimes of each energy level is as follows:

1 = 1 ! + 1 "! The reciprocals of the lifetimes are equal to the rate of decay. Therefore, ')*) ='! +'"!, the total rate of decay is equal to the sum of the non-radiative and radiative decay rates (Quimby,2006).

The ion populations for each level can be determined by solving the rate equations for the

steady-state (setting the change of level population per unit time to zero). Since we are assuming

that there is no stimulated emission of the signal (i.e. lasing is not yet occurring in the material),

we can further simplify the equations using the pump rate variables outlined above and set the

emission rate to zero. The 3H5 level decays immediately and non-radiatively because it has a very

high radiative lifetime and low non-radiative lifetime. This means that we do not need a separate

rate equation for level 3, but can just assume that any transition to level 3 immediately goes to

level 2. Therefore, the rate equations are simplified to:

0 = ��ℎ�� − �� − �� !� − �� "!�

17

0 = �%�� !� + �� "!� − �% % 0 = �� !� +�% % − ��ℎ�� − ��

Solving for �% and �� using only the �� concentration: �% = �� % ,�% !� + 1 "!�-

�� =�� ,./�01�.2�01� + 34151.2�01�67- Since�� + �% + �� = � and the dopant concentration $ is known, the �� population

can be determined by solving these three equations simultaneously. Once �� population is determined, it can be substituted into the previous two equations to solve for the populations of

the other two levels.

Once the ion level populations are determined, the gain coefficient at the 800nm

transition can be determined utilizing the absorption and emission data obtained from

measurements and calculations. Again, the gain coefficient is given by the following equation:

�� = �� − �� If the gain coefficient is positive, a net gain is occurring at the signal wavelength. If the

gain coefficient is negative, there is a net absorption at the signal wavelength.

The absorption and emission cross-sections are directly related to each other via the

reciprocity method:

�� = ��[9:9;]=>?@A�3B0 �CDE

Where FGH is the zero line energy (which is defined as the difference in energy between the lowest energy level of the 3I� level and the lowest level of the ground state), 9: and 9; are the partition functions of the lower and upper state (Walsh, 1998), � is Planck’s constant, � is the

18

speed of light, JKis Boltzmann’s constant, and � is the temperature of the crystal during the measurement in Kelvins (room temperature is approximately 293K). This equation was used to

check the experimental results of the emission cross-section versus a theoretical result obtained

by the absorption cross-section and the calculations are explained in further detail in the

methodology section.

Lastly, the most common comparative figure of merit used to analyze any laser transition

is the quantum efficiency, ϕ. The quantum efficiency of an upper laser level is defined as the rate of radiative decay divided by the total rate of any decay and can be written in terms of the upper

state lifetimes (Quimby, 2006).

M = ! Where τ is the total fluorescence lifetime of the upper laser level, and ! is the radiative

lifetime of the upper laser level.

The absorption, emission, and lifetime data from the experiments performed on the

various host materials (and outlined in the methodology section) will be used with these

equations to analyze the change in the level concentrations and subsequently in the net gain that

occurs with various pumping powers, as well as the overall efficiency the best host material for a

laser at this transition.

��

Several important characteristics go into choosing the appropriate host material in any

solid-state laser system. Host materials must have low reflectivity and high absorption at the

pump wavelength. They must have a high thermal conductivity in order to disperse heat, because

any pump energy that decays non-radiatively will be turned into heat. This is extremely

important when operating at higher powers. Heat can cause stress on the host material and

change the properties of the material affecting the quality of beam, output power, and fracturing

of the material itself (Hecht, 2008).

19

Crystals, in particular, dissipate heat better than glass (thermal conductivity of glass is

approximately 1.5 W/m*K). In this application – where the desire is to be able to have a high

power laser – crystalline hosts were chosen. The crystals chosen for this project were chosen

based upon their thermal and mechanical properties as well as their high branching ratios for the

3I� – 3IN transition. They are listed in the following table, along with the important characteristics of each material (see Table I).

TABLE I. Properties of Host Materials

Host

Crystal

Crystalline

Structure

Approx. Thermal

Conductivity(W/mK)

Concentration

N (10²⁰/cm³)

Est. Refractive

Index

(n)

Branching Ratio

(β) of 3H4 –

3H6

(%)

YLiF Tetragonal 11.7 2.75 1.45 87 (Walsh, 98)

YVO4 Tetragonal 5.23 2.48 2.00 90 (Ermeneux, 97)

YAlO Orthohombic 11.7(a),10(b),13.3(c) 3.90 1.94(b), 1.97(c) 84 (Caird, 75)

YAG Cubic 11.2 2.75 1.82 84 (Caird, 75)

The crystalline structure of the material is important. Crystals that do not have a cubic

structure will have the measurements for absorption and emission cross section polarized to

account for their birefringence. Birefringence means that the refractive index of the material is

dependent upon the direction of the incident beam’s electric field (polarization) (Quimby, 2006).

The different polarizations will be designated as transverse electric, TE, or transverse magnetic,

TM, throughout this paper.

20

��+��

In order to properly evaluate each host material, the absorption and emission spectra need

to be acquired as a function of wavelength for each individual crystalline host at room

temperature, or approximately 300K. The absorption, emission, and lifetime measurements were

all performed in the facilities at WPI. Additional absorption measurements at a higher resolution

(~.3nm) were made at MIT Lincoln Laboratory using a state of the art spectrometer. With these

higher resolution spectra acquired, the reciprocity method was able to be used to calculate the

emission spectra at the same resolution. To validate the use of reciprocity, a lower resolution

(~1.5nm) emission measurement was obtained at WPI and compared to a calculated spectrum.

The reciprocity method was only used on the Tm:YVO4 and Tm:YLiF crystals, because the zero

line energy and values of the partition functions were able to be obtained from the literature.

After the data was collected, the gain cross-section and lifetime values were used in the

rate equations for further analysis, and a determination was made of which material would allow

for the most efficient lasing at this transition.

��+��%(��9��

For the absorption measurements performed on the crystals at WPI, a single beam

spectrophotometer was set up (see Figure 5). A tungsten halogen bulb was used a light source,

the light was collimated with a lens, passed through a chopping wheel, and was focused with a

lens onto the sample. The light exiting the sample was collected by another lens that focused it

onto the entrance slit of a Jarrell-Ash spectrometer with dispersion of approximately

1mm/3.2nm. This dispersion means that if the slit width is set at 1mm, the resolution of the

spectra obtained will be 3.2nm. The grating inside the spectrometer scans through the desired

wavelength range and the light exits through the output slit onto a photodiode. This photodiode’s

signal is then amplified by a lock-in detector. The calculated emission spectra from the WPI

data were used only in comparison to the spectral shape and those values were not used in

analysis (only the measured spectra was used).

21

Due to the varying lattice structures of the different host materials chosen for analysis,

the absorption measurements were polarized for any crystals that are birefringent - such as the

tetragonal crystals or orthorhombic. The spectrometer at MIT had a built in polarizer for such

measurements. For the setup at WPI, a polarizing crystal was placed before the sample in the

beam path. For both sets of these measurements, a second handheld polarizing film was used to

make sure that the crystals are properly aligned so that the light propagates directly down the

appropriate optical axis. The film is placed in the path of light after the crystal. The crystal is

aligned properly if all the light is extinguishable by turning the handheld polarizing film 90˚

from the polarizer located before the crystal.

Figure 5. Constructed one-channel spectrophotometer

While performing the measurements at WPI, it was difficult to get the necessary

resolution to view the absorption peaks of the crystals. The signal to noise ratio was poor under a

slit width of .5mm, which only allows for an approximate resolution of 1.6nm. For proper

analysis, it was necessary to obtain measurements with a .3nm resolution. Utilizing the facilities

22

of the Laser Technology and Applications Group at MIT Lincoln Laboratory, further

measurements were able to be made using their Perkin Elmer Lambda 1050 Spectrophotometer.

The spectrophotometer measures the change in transmission as a function of the

wavelength and then analyzed using Beer’s Law which is given by:

��O = P = Q=ARH Where, for these experiments, S is the absorption coefficient, % is the thickness of the

sample, P is the fraction of light transmitted through the sample at a given wavelength, and Q is a function which may depend weakly on wavelength based on the transmission (due to the

reflection at the two surfaces and other effects not related to the rare earth absorption). This

function C, results in a sloping baseline which needs to be divided by the raw transmission to

obtain the actual cross section. This will be discussed in more detail below. Rearranging the

above equation we can solve for the absorption coefficient as a function of wavelength.

Taking the absorption coefficient and dividing by the concentration of dopant (ions per

cubic centimeter), provides the absorption cross-section as a function of wavelength.

S�T��U�V W.2XY�0� For each of the absorption spectra obtained, a baseline had to be adjusted from the raw

spectra data. In order to do this, the raw data was plotted in excel and a trend line was applied to

flat sides of the absorption feature (see Figure 6). The trend line is the function C, which is the

baseline. Depending on where you apply the baseline adjustment it is either subtracted or divided

from the raw data. For the measurements done at WPI, the reduction was applied to the

absorption coefficient data calculated by the measured intensities. Therefore we had to subtract

the baseline from the calculated absorption coefficient data:

Zln � ��O�−] ^ − ln�Q� = S�T�� For the measurements done at MITLL, the baseline adjustment was applied to the raw

transmission data. For those measurements this equation was used to subtract the baseline:

Where C, represents the function

C is the baseline adjustment needed for these measurements

Figure 6. Example of MIT Baseline

transmission data on either side of the absorption feature)

��+��

As stated in the background, the emission

the data obtained from the absorption measurements and using the

�The only two crystals able to be calculated using the reciprocity method, were the

Tm:YVO4 and Tm:YLiF crystals.

Tm:YLiF, the ratio of the partition functions

12599 _À�, the value of CXE3B is 204 approximately 293K). For the YVOCXE3B is 204 _À�, and the ratio of the partition functions is

23

For those measurements this equation was used to subtract the baseline:

,PQ- = =ARH function referred to before. Dividing the transmission, T, by this

for these measurements in this case.

Baseline Adjustment (C(λ) is the trend line determined by plottin

transmission data on either side of the absorption feature).

�9��

As stated in the background, the emission spectra can be theoretically calculated by using

the data obtained from the absorption measurements and using the reciprocity method.

�� = ��[9:9;]=>?@A�3B0 �CDE

The only two crystals able to be calculated using the reciprocity method, were the

and Tm:YLiF crystals. Utilizing previous research done at room temperature on

Tm:YLiF, the ratio of the partition functions is equal to 0.9884, the value of FGH is 204 _À� (Walsh, 1998) (where T for all measurements was

For the YVO4, the value of FGH is given as 12523 _À�, the value of , and the ratio of the partition functions is approximately 0.9880 also

For those measurements this equation was used to subtract the baseline:

referred to before. Dividing the transmission, T, by this

Adjustment (C(λ) is the trend line determined by plotting the

can be theoretically calculated by using

.

The only two crystals able to be calculated using the reciprocity method, were the

Utilizing previous research done at room temperature on

is given as

re T for all measurements was

, the value of

also (Lisiecki,

24

2006).

��+��9��

Another method and the one that was utilized in this project, to obtain the relative

emission spectra, is to pump the samples with a diode laser (690nm – outside the wavelength

range of interest) and measure the emission using a spectrometer (see Figure 7). The laser light is

collimated through a lens, passes through the chopping wheel, and using another lens focused

onto the sample. For this setup, it is important for none of the pump laser light to get into the

spectrometer. This can be achieved using a beam block or filters, but an easier method (and the

one used in these experiments is to use a mirror to reflect the beam downward onto the sample.

The fluorescence exits the side closest to the beam, passes through a polarizer (only for the

birefringent crystals), is collected by another lens, and focused onto the slit of the spectrometer.

The grating inside moves through the desired wavelength range and the light passes through the

exit slit onto the photodiode. The signal is amplified using the lock-in amplifier and sent to the

data acquisition board connected to the computer.

Figure 7. Emission Measurement Setup

The emission measurements obtained in this way are relative measurements and give the

25

spectral shape of the cross-section. The absolute value of the emission is unknown because, by

using the method outlined previously, only a portion of the emitted fluorescence is being

collected and focused into the spectrometer (Martin, 2006).

To correct for the spectral dependence of grating and detector, a blackbody emission

fluorescence measurement was also taken. In the exact place of the crystal, the tungsten filament

(inside the halogen bulb) is placed. Three measurements (TE, TM, unpolarized) were obtained.

The ratio of the measured signal and the measured blackbody signal multiplied by the known

spectral density of blackbody radiation over the particular wavelength range provides the true

intensity that is emitted by the crystal sample. The equation for the blackbody spectral density, as

a function of wavelength, is:

a0�� = ab�c� �c�� a0�� = 8eℎ_#_#�# f 1=� 3B0CE� − 1g h _�%i

Where the � is the temperature of the filament, estimated to be 2900K, is Boltzmann’s

constant, � is Planck’s constant, and � is the speed of light (in a vacuum) (Quimby, 2006).

Multiplying this by the ratio of signals obtained gives a relative intensity:

�� = jkl3BmBm0m n �� opqrs�A�t h B0uiv [ w�0�wDD�0�] The relative emission spectral shape (ss), �x�� is given by the following equation:

�x�� = [0y"u]�� = jkl3BmBm0m n �� opqrs�A�t h B0uiv [ w�0�wDD�0�] Where � is the average refractive index of the material - see Table 1 (Martin, 2006). Once

the spectral shape of the cross section has been determined a background subtraction must be

applied. This background subtraction removes any signal that is not part of the crystal

fluorescence that may have entered the detector (such as ambient light). After performing the

background subtraction, an approximate value of the emission cross section can be determined

26

by utilizing the following relationship:

z{�x�� = {�� = |:|; {�� Where &�is a constant of proportionality that relates the integral of the spectral shape to

the integral of the emission cross-section. The }~} is the ratio of degeneracy of this particular

transition and can be determined by:

}~} = �%��%�� = �%∗N��%∗�� = 1.4444 Where� ' is the total angular momentum of the 3IN level and� '( is the total angular

momentum of the 3I� level. This constant, &, can be obtained by integrating the measured absorption cross-section

over the wavelength range of interest, multiplying by this ratio, and then dividing by the integral

of the measured spectral shape over the same wavelength range. Multiplying each of the spectral

shape values by this constant provides an approximation for the actual value of the emission

cross section (Martin, 2006).

.��

� The lifetime measurements were conducted by using a diode laser of nominal wavelength

690nm to pump a sample of each host material. The pump laser was pulsed by placing a chopper

wheel in the initial beam path. Sets of lenses were used to collimate the beam throughout the

setup and two band pass filters will be used to filter out any light below 800nm (see Figure 8). A

silicon photodiode was used to detect the fluorescence, convert it into a voltage signal which can

then be viewed as a function of time by utilizing an oscilloscope.

27

�

Figure 8. Lifetime Measurement Setup

Once the signal was acquired, the data was plotted in excel and graphed as a function of

time. The baseline voltage is subtracted from the signal voltage in order to bring the signal to

zero, and then the resultant voltage is graphed in a logarithmic scale (see Figure 9). The equation

for determining this lifetime is as follows:

�� − �� = O=A)6 Where V(t)is the signal voltage at time, �, �� is the baseline voltage at time, �, O is the

voltage at time � = 0, and τ is the fluorescence lifetime.

Figure 9. Example of

The slope of the line of the lower right hand graph

fluorescent lifetime and can often be determined visually. Due to time constraints, only the

lifetime for Tm:YLiF was measured. The upper

from previous literature.

28

. Example of Tm:YLiF Lifetime Measurement Calculations

of the lower right hand graph is the negative reciprocal of the


lifetime for Tm:YLiF was measured. The upper-state lifetime of the other crystals were sourced

is the negative reciprocal of the


state lifetime of the other crystals were sourced

29

�:��!��

%(��!��

30

TABLE II. WPI Cross-Sectional Data for TE Polarization & Unpolarized (YAG only)

Host

Cross Section (10----21212121 cm²) Absorption

Emission

(Measured) Absorption

Emission

(Measured)

σ(790nm) σ(790nm) σ(820nm) σ(820nm)

YVO4 15.56±0.5 6.87 ±0.6 2.67 ±0.5 10.80 ±0.6 YLiF 3.11 ±0.05 1.54 ±0.06 .502 ±0.05 1.76 ±0.06

YAlO-c 2.08 ±0.05 .196 ±0.06 .891 ±0.05 2.75 ±0.06 YAlO-b 2.08 ±0.05 .552 ±0.06 .876 ±0.05 3.27 ±0.06

YAG 2.08 ±0.07 1.54 ±0.08 .256 ±0.07 3.58 ±0.08

TABLE III. WPI Cross-Sectional Data for TM Polarization

Host

Cross Section (10----21212121 cm²) Absorption

Emission

(Measured) Absorption

Emission

(Measured)

σ(790nm) σ(790nm) σ(820nm) σ(820nm)

YVO4 11.09 ±0.3 2.47 ±0.32 2.45 ±0.3 12.18 ±0.32 YLiF 2.40 ±0.05 1.89 ±0.06 .337 ±0.05 2.32 ±0.06

YAlO-c 1.77 ±0.05 1.05 ±0.06 5.14 ±0.05 2.88 ±0.06

Since the emission measurements were scaled using the approximation method (outlined

in the methodology section), even though the error propagating from the trend line fit to the

background reduction was considerably less (on average ±0.01 10A%O _`%), this error coupled with the error from the absorption measurements leads to a slightly higher uncertainty of ±0.032 10A%O _`% for Tm:YVO4. Since the emission cross section is directly related to the absorption cross section, the highest values of emission cross section measured at the pump

wavelength and desired emission wavelength were the Tm:YVO4 (from the TM polarization) at

2.4710A%� _`% ± 0.032 10Arespectively. Examples of the measure

shown below (see Figure 9). The emission measurement of the TM polarization for the

Tm:YAlO propagating through the B

measurement for Tm:YAlO propagating through C

Utilizing the reciprocity method for the Tm:YVO

cross section – evident in Figure 10

responsible for the loss of some of the finer features of the cross se

spectral shape of both the measured and calculated spectra, it can be seen that both spectra h

the emission starting at approximately 785nm and a peak at approximately 810nm.

Figure 10. Example Absorption, Measured Emission, and Calculated Emission

Only the Tm:YVO4 and Tm:YLiF

reciprocity method. For the purpose of comparative analysis with the other crystals

measured cross sectional data was utiliz

31

A%O _`% and 1.2210A%O _`% ± 0.032 10Examples of the measured absorption and emission graphs for TM:YVO

The emission measurement of the TM polarization for the

propagating through the B-axis was unnecessary because it was the same as the

Tm:YAlO propagating through C-axis.

method for the Tm:YVO4 gave an approximation of the emission

e 10. The low signal to noise ratio in the measured emission is

responsible for the loss of some of the finer features of the cross section, but by comparing the

spectral shape of both the measured and calculated spectra, it can be seen that both spectra h

the emission starting at approximately 785nm and a peak at approximately 810nm.

. Example Absorption, Measured Emission, and Calculated Emission Graphs

and Tm:YLiF had their emission spectra calculated using the

or the purpose of comparative analysis with the other crystals

measured cross sectional data was utilized for subsequent calculations.

10A%O _`% d absorption and emission graphs for TM:YVO4 are

The emission measurement of the TM polarization for the

axis was unnecessary because it was the same as the TE

approximation of the emission

. The low signal to noise ratio in the measured emission is

by comparing the

spectral shape of both the measured and calculated spectra, it can be seen that both spectra have

(WPI)

had their emission spectra calculated using the

or the purpose of comparative analysis with the other crystals only the

32

Although the reciprocity method was a good approximation for the Tm:YVO4 because of

a higher signal to noise ratio on the absorption measurements, the calculated Tm:YLiF emission

spectra had too much noise to be utilized effectively for comparison. This was due to the lower

signal to noise ratio in the absorption measurement. The higher amount of noise is exponentially

increased in the emission calculation (see Appendix A).

%(��!��1��

� In order to get an accurate graphical representation of the absorption and emission cross

sections of the 3I� level, the measurements had to be done with a resolution of 0.3nm or higher. Utilizing the state of the art spectrometer at MIT (Lincoln Laboratory) each crystal’s absorption

features was analyzed. The data to calculate the emission cross section using reciprocity method

was only obtained for the Tm:YVO4 and Tm:YLiF. Therefore, only those two crystals were

comparatively analyzed at each polarization from this data (see Table IV & Table V).

TABLE IV. MIT Cross-Sectional Data for TE Polarization

Host

Cross-sections (10----21212121 cm²) Absorption

Emission

(Calculated) Absorption

Emission

(Calculated)

σ(790nm) σ(790nm) σ(820nm) σ(820nm)

YVO4 10.50 ±0.2 5.25 ±0.2 1.54 ±0.2 7.47 ±0.2 YLiF 4.28±0.02 3.16 ±0.02 .304 ±0.02 2.18 ±0.02

TABLE V. MIT Cross-Sectional Data for TM Polarization

Host

Cross-sections (10-21

cm²)

Absorption Emission

(Calculated) Absorption

Emission

(Calculated)

σ(790nm) σ(790nm) σ(820nm) σ(820nm)

YVO4 25.39 ±0.2 12.74 ±0.2 1.52 ±0.2 7.37 ±0.2 YLiF 3.81 ±0.02 2.82 ±0.02 2.15 ±0.02 1.54 ±0.02

Due to the higher resolution and high signal to noise ratio, the graphs for these

measurements were much smoother than

were able to be determined for both the absorption and emission cross sections

For the TM:YVO4 and and Tm:YLiF, the

leading to an uncertainty in the value of the cross section

Figure 11. Absorption and

After reviewing both the cross sectional resuls for both the WPI and MIT measurements,

a determination was made to use the MIT data for comparative analysis further in this section

when comparing the figures of merit.

.��!��

Most of the total fluorescence

from the literature (see Table VI). Only the Tm:YL

the laboratory. The upper state fluorescence lifetime was

33


measurements were much smoother than the measurements obtained at WPI, and the peak values

were able to be determined for both the absorption and emission cross sections (see Figure 11

and and Tm:YLiF, the deviation from the trend line was approximately

in the value of the cross section of approximately ±0.02

Absorption and Calculated Emission Graphs (MIT)


de to use the MIT data for comparative analysis further in this section

when comparing the figures of merit.

total fluorescence lifetime data and radiative lifetime data were

Only the Tm:YLiF fluorescence lifetime of was measured

upper state fluorescence lifetime was determined to be 2000μs ±


the measurements obtained at WPI, and the peak values

(see Figure 11).

approximately .1%, 10A%O_`%.


de to use the MIT data for comparative analysis further in this section

determined

was measured in ±20μs (see

Figure 12) by taking the negative reciprocal of the slope of the logarithmic plot.

fluorescence and radiative lifetimes were determined, the non

determined using the relationship outlined in the methodology section. The total lifetime of the

intermediate level 3F4 level was also

comparative analysis utilizing the rate equations from the background section.

TABLE VI. Lifetime Data (non-

measured

3H4 Lifetimes (

Host τ

YVO4 176 (Lisiecki, 06)

YLiF 2000

YAlO 500(Caird, 75)

YAG 797(Caird,75)

Figure 12.Tm:YLiF 3H4 Fluorescent Lifetime Measurement at 293K (where V is signal, B is baseline).

With all the experimental data collected, the figures of merit were then calculated based

upon the data acquired and a comparative analysis discussed in the following section.

%��=��

Utilizing the rate equation analysis outlined in the

determine the gain coefficient at various pumping powers were determined (see Appendix B

34

) by taking the negative reciprocal of the slope of the logarithmic plot.

fluorescence and radiative lifetimes were determined, the non-radiative lifetime could be


level was also obtained from the literature, because it is necessary for

comparative analysis utilizing the rate equations from the background section.

-radiative calculated in this work, fluorescence of YLiF

measured in this work)

Lifetimes (μs) 3F4 Lifetime

τ[nr] τ[r]

528 264 (Lisiecki, 06) 1923 (Lisiecki, 06)

22000 2200 (Walsh,98) 9329

1175 870 (Caird, 75) 5000

1700 1500 (Caird,75) 9900

Fluorescent Lifetime Measurement at 293K (where V is signal, B is baseline).



rate equation analysis outlined in the background section, calculations to

determine the gain coefficient at various pumping powers were determined (see Appendix B

) by taking the negative reciprocal of the slope of the logarithmic plot. Once the

radiative lifetime could be


ecause it is necessary for

, fluorescence of YLiF

Lifetime (μs)

τ

(Lisiecki, 06)

(Walsh, 98)

(Barnes, 06)

9900 (Caird,75)

Fluorescent Lifetime Measurement at 293K (where V is signal, B is baseline).



background section, calculations to

determine the gain coefficient at various pumping powers were determined (see Appendix B –

35

Sample Calculations). Several figures of merit were determined utilizing the gain coefficient,

such as the maximum gain coefficient and threshold gain coefficient, the maximum gain cross

section, the gain coefficient per unit pump power (at pump saturation), and the gain coefficient

per unit of absorbed power per unit length.

Additionally, as noted previously, the quantum efficiency of a laser is determined by the

ratio of radiative decay to total decay and is a common figure of merit for a laser transition.

Utilizing the lifetime data obtained from previous research and the measurement obtained

experimentally, the quantum efficiency was determined for each crystal (see Table VII). Here,

the highest quantum efficiency is present in Tm:YLiF; it is common for laser materials to have

between .40 and .100 efficiency (RP, 2014). Therefore, all the materials tested had acceptable

quantum efficiency.

TABLE VII. Quantum Efficiency of each Host

Host Quantum Efficiency (φ)

YVO4 0.667

YLiF 0.909

YAlO 0.575

YAG 0.531

By incrementally increasing the pump power, we can view the change in level

populations and subsequently the increase in gain coefficient. At a certain point, the gain

coefficient reaches a maximum point, where it no longer increases (see Figure 13). Incrementally

increasing the pump power also allows us to find the gain pump threshold – the approximate

power at which the gain coefficient is equal to zero and, above which, lasing can occur. These

values were calculated utlizing both the MIT data and WPI data (see Table VIII). The Tm:YAlO

at TM polarization never reaches a positive gain coefficient because the value of the absorption

cross section is higher than the emission cross section at the signal wavelength (see Table III).

TABLE VIII. Maximum Gain Coefficients and Threshold Power

TE Polarization or Unpol

Host

Max Gain

Coefficient

γ(cm¯¹)

YVO4 0.282

YLiF 0.198

YVO4 0.411

YLiF 0.168

YAlO 0.183

YAG 0.108

The values for YLiF and YVO

accurate because they were calculated from the higher resolution absorption measurements. For

the purpose of further analysis, we will assume these measurements to be a more accurate

representation of the actual values. Also, the TE polarization will only be used for further figure

of merits, because the max gain is higher for the Tm:YLiF, Tm

polarization.

Figure 13.Gain coefficients at saturation and near threshold pump power

36

Gain Coefficients and Threshold Power for each Host (rod dia.

TE Polarization or Unpol (YAG) TM Polarization

Coefficient

Threshold

Pump Power

~(kW)

Max Gain

Coefficient

γ(cm¯¹)

Threshold

Pump ~(kW)

MIT Data

15.7 0.279 6.5

2.3 0.140 2.6

WPI Data

12.7 0.515 13.6

6.8 0.204 4.3

35 -0.013 N/A

5.8 N/A N/A

and YVO4 provided by the MIT measurements were slightly more



e actual values. Also, the TE polarization will only be used for further figure

in is higher for the Tm:YLiF, Tm:YAlO, and Tm:YVO

Gain coefficients at saturation and near threshold pump power for all hosts at TE polarization

(rod dia. 0.4cm)

provided by the MIT measurements were slightly more



e actual values. Also, the TE polarization will only be used for further figure

:YAlO, and Tm:YVO4 at this

for all hosts at TE polarization

37

The maximum gain coefficient divided by the total concentration of thulium ions (see

how to calculate concentration in Appendix B) we can determine the maximum gain cross-

section (see Table IX).

TABLE IX. Net Gain Per Unit of Concentration

Host

Max Gain

Coefficient

γ(cm¯¹)

Concentration

(N) (10²⁰cm-³)

Gain/

Total

Concentration

(10-20

cm2)

MIT Data

YVO4 0.282 2.48 .114

YLiF 0.198 2.75 .072

WPI Data

YAlO 0.183 3.9 .046

YAG 0.108 2.75 .039

� It can be seen from this data that the maximum gain coefficient of Tm:YVO4 is almost

double that of the other three crystals. It can be seen (from Figure 12) that the Tm:YLiF crosses

the threshold for lasing at the lowest pump power (~2.5kW). In contrast, the Tm:YAlO crosses

the threshold for lasing at a much higher value of approximately 35kW. The maximum gain

cross section (at the emission wavelength) is the highest in the Tm:YVO4 due to the gain

coefficient being slightly higher but also the number of ions per volume of Vanadate is less than

that of the three other crystals.

The point at which the change in gain coefficient becomes negligible in comparison to

the increase in pumping power is known as saturation. The power where the gain becomes

significantly saturated is known as the saturation power and the crystal becomes increasingly

unable to absorb additional pump power above this saturation point. The gain coefficient at this

saturation power, divided by either the incident or the absorbed pump power is an excellent way

to compare the host materials and choose the best material for the desired application of interest.

In the case of our interest, we desire a material that has a highest net gain at the lowest possible

pump power. Using the graph below we can estimate the point at which significant saturation

occurs, and we can determine the incident pump power and absorbed power there to compare the

materials(see Figure 14).

38

Figure 14. Estimated Pump Powers for Relative Gain Saturation

Using the value for gain coefficient at this estimated power and dividing by these

corresponding estimated pump and power absorbed per unit length will give us an estimation of

the gain per unit of power (see Table X).

To calculate the figure of merit defined as the gain coefficient per unit length divided by

the absorbed power per unit length, we use the following equation: �T��" = �� − �� Where �) is the fractional thickness, we use 1cm for our calculations (see Appendix B).

TABLE X. Gain Coefficient per unit Saturation Pump Power and Power Absorbed

Host

Gain

Coefficient

(cm¯¹)

Pump Power

~(kW)

Gain

/Pump

Power

(kW*cm)-1

Fraction

Of Power

Absorbed

per unit

length (cm-

1)

Gain coefficient

/ Power

Absorbed (per

unit length)

(kW)-1

YVO4 0.215 100 .0022 .27 .008

YLiF 0.160 35 .0046 .157 .029

YAlO 0.09 85 .001 .147 .007

YAG 0.075 40 .0019 .103 .018

Utilizing this figure of merit as a comparison, we can see that although the Tm:YVO4 has

a higher maximum gain coefficient, its efficiency with respect to pump and absorption power per

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60 70 80 90 100

Gai

n Co

effic

ient

(cm¯¹¯¹ ¯¹¯¹)

Pump Power (kW)

Estimated Saturation Pump Power

Tm:YVO4 (MIT)

TM:YLiF (MIT)

Tm:YAlO

Tm:YAG

39

unit length is lower than that of Tm:YLiF. The Tm:YAG crystal has a high gain to absorption

ratio, as well, but it is limited by gain saturation at lower power levels. Based on all the above

analysis, a recommendation can now be made for future testing.

��;�!��

Upon completion of this project, there are several observations that can be made with

regards to the methodology and results.

The rate equations are a good tool to use in evaluating a laser transition. By utilizing

measured emission and absorption cross sections at high resolution and lifetime data, we can

estimate the change in level populations with respect to various pump and absorption powers and

comparatively analyze the net gain of the transition.

The reciprocity method of calculating the emission cross section is valid only if the

absorption cross section does not have a low signal to noise ratio. For crystals with a sub-level

energy structure, such as the ones analyzed in this report, the resolution of the absorption

measurements has to be roughly .3nm or higher.

The highest quantum efficiency does not necessarily mean that the particular crystal will

have the highest gain. In this case, the Tm:YLiF had a quantum efficiency of .91 whereas the

Tm:YVO4 had an efficiency of .67. However, the Tm:YVO4 had a maximum gain coefficient

almost double the value of the Tm:YLiF. The quantum efficiency comparison is important

because it tells us that Tm:YLiF produces less heat, which would have to be removed from the

laser system, via some form of cooling.

Based on all the results analyzed, the crystal I would recommend for further testing is the

Tm:YLiF. It can be seen from the results that Tm:YLiF has the lowest pump power at threshold,

best gain to pump power ratio, best gain to fractional absorbed power ratio, and the quantum

efficiency is the highest for all the measured crystals. This means that any laser system utilizing

Tm:YLiF will require less overall power than the other three.

40

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lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4,” '��

#��., Vol. 83, No. 5, pp. 2772-2787, March 1 1998.

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